Le Bernardin, which just retained its three Michelin-star rating, has long had a happy problem: demand for private dining ridiculously exceeds supply.

The fabled 110-seat seafood restaurant has had a second-floor “Salon” seating 80 since 2000. But even though chef Eric Ripert says, “It changed our life,” and its success helped Ripert and co-owner Maguy Le Coze keep prices relatively low in their public dining room (there’s even a $45 lunch in the lounge), they hungered for a larger facility for celebrations such as weddings and corporate gatherings.

Enter new Privé. Although the new Aldo Sohm Wine bar has drawn more media coverage, Privé is by far the larger portion of Le Bernardin’s first-time ever expansion inside the AXA tower and more crucial to the great restaurant’s future.

Installed on the second floor of the AXA tower’s eastern section across the pedestrian arcade from the main restaurant, Privé can seat 150 to 170 in the space that was previously Italian eatery Piano Due. For cocktails only it can hold 300.

Privé, served by its own new state-of-the-art kitchen, is already busy with bookings although it’s only been open a few weeks. Ripert is high on its future.

“It has the potential to generate about one-third of our main dining room revenue, but will yield a higher profit because the regular dining room runs on a lower margin,” he said.

The sleek space was designed by Bentel & Bentel Architects to reflect the mood of Le Bernardin — including teak wood, spiraling metal artwork and a surf image by Brooklyn painter Ran Ortner which echoes the one on the dining room’s rear wall.

Guests enter through a ground-floor elevator bank accessed by its own door in the arcade to the left of the wine bar.

Ripert and Le Coze have long declined to say how much the expansion cost, but real-estate insiders put the total buildout for the two new venues at around $8.5 million.

Although they’re similarly shy about discussing their arrangement with landlord AXA, industry scuttlebutt has long been that Le Bernardin, and now its satellites, pays a percentage of gross revenue rather than rent.

Customers have long clamored to rent Le Bernardin for their private events, but Ripert was loath to give up the whole dining room more than once or twice a year. “Our regular clientele doesn’t like that,” he said.